Interactions between Harmonic Analysis and Operator Theory
Ivan G. Todorov · Bulgarian Digital Mathematics Library (BulDML) at IMI-BAS (Institute of Mathematics and Informatics) · 2015
The artice is a survey of several topics that have led to fruitful interactions between Operator Theory and Harmonic Analysis, including operator and spectral synthesis, Schur and Herz-Schur multipliers, and reflexivity.Some open questions and directions are included in a separate section. Introduction.Functional analytic methods have proved fruitful in Abstract Harmonic Analysis [19], [38], [8]. On the other hand, operator algebras constructed from topological groups have served as important examples in Operator Theory [27].The aim of this article is to present some aspects of the symbiosis between the two areas which, broadly speaking, starts from Varopoulos' and Arveson's seminal papers [38] and [1].We will summarise results by a number of authors, which can be grouped under the following headings:• Spectral and operator synthesis;